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A fifth-order shock capturing scheme with two-stage boundary variation diminishing algorithm
- Source :
- Journal of Computational Physics. 386:323-349
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 2019.
-
Abstract
- A novel 5th-order shock capturing scheme is presented in this paper. The scheme, so-called P 4 T 2 − BVD (polynomial of 4-degree and THINC function of 2-level reconstruction based on BVD algorithm), is formulated as a two-stage spatial reconstruction scheme following the BVD (Boundary Variation Diminishing) principle that minimizes the jumps of the reconstructed values at cell boundaries. In the P 4 T 2 − BVD scheme, polynomial of degree four and THINC (Tangent of Hyperbola for INterface Capturing) functions with two-level steepness are used as the candidate reconstruction functions. The final reconstruction function is selected through the two-stage BVD algorithm so as to effectively control both numerical oscillation and dissipation. Spectral analysis and numerical verifications show that the P 4 T 2 − BVD scheme possesses the following desirable properties: 1) it effectively suppresses spurious numerical oscillation in the presence of strong shock or discontinuity; 2) it substantially reduces numerical dissipation errors; 3) it automatically retrieves the underlying linear 5th-order upwind scheme for smooth solution over all wave numbers; 4) it is able to resolve both smooth and discontinuous flow structures of all scales with substantially improved solution quality in comparison to other existing methods; and 5) it produces accurate solutions in long term computation. P 4 T 2 − BVD , as well as the underlying idea presented in this paper, provides an innovative and practical approach to design high-fidelity numerical schemes for compressible flows involving strong discontinuities and flow structures of wide range scales.
- Subjects :
- Numerical Analysis
Polynomial
Physics and Astronomy (miscellaneous)
Applied Mathematics
Boundary (topology)
Tangent
Upwind scheme
010103 numerical & computational mathematics
Function (mathematics)
Classification of discontinuities
01 natural sciences
Computer Science Applications
Hyperbola
010101 applied mathematics
Computational Mathematics
Discontinuity (linguistics)
Modeling and Simulation
0101 mathematics
Algorithm
Mathematics
Subjects
Details
- ISSN :
- 00219991
- Volume :
- 386
- Database :
- OpenAIRE
- Journal :
- Journal of Computational Physics
- Accession number :
- edsair.doi.dedup.....6072c9379e1d3f6204d8c764ef2bf87e